(1) 2a的m+1次方+4a的m次方-2a的m-1次方 (2)x的四次方-4x的平方+4x-1

问题描述:

(1) 2a的m+1次方+4a的m次方-2a的m-1次方 (2)x的四次方-4x的平方+4x-1

(1)
2a^(m+1)+4a^m-2a^(m-1)
=2a^(m-1)(a^2+2a+1)
=2a^(m-1)(a+1)^2
(2)
x^4-4x^2+4x-1
=x^4-(4x^2-4x+1)
=(x^2)^2-(2x-1)^2
=[x^2+(2x-1)][x^2-(2x-1)]
=(x^2+2x-1)(x^2-2x+1)
=(x^2+2x-1)(x-1)^2